/*
 * This file is part of the GROMACS molecular simulation package.
 *
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 * Copyright (c) 2001-2004, The GROMACS development team.
 * Copyright (c) 2013,2014,2015,2016,2017 The GROMACS development team.
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 * Mark Abraham, David van der Spoel, Berk Hess, and Erik Lindahl,
 * and including many others, as listed in the AUTHORS file in the
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#include "gmxpre.h"

#include "orires.h"

#include <climits>
#include <cmath>

#include "gromacs/gmxlib/network.h"
#include "gromacs/linearalgebra/nrjac.h"
#include "gromacs/math/do_fit.h"
#include "gromacs/math/functions.h"
#include "gromacs/math/vec.h"
#include "gromacs/mdrunutility/multisim.h"
#include "gromacs/mdtypes/commrec.h"
#include "gromacs/mdtypes/fcdata.h"
#include "gromacs/mdtypes/inputrec.h"
#include "gromacs/mdtypes/mdatom.h"
#include "gromacs/mdtypes/state.h"
#include "gromacs/pbcutil/ishift.h"
#include "gromacs/pbcutil/pbc.h"
#include "gromacs/topology/ifunc.h"
#include "gromacs/topology/mtop_util.h"
#include "gromacs/topology/topology.h"
#include "gromacs/utility/arrayref.h"
#include "gromacs/utility/fatalerror.h"
#include "gromacs/utility/pleasecite.h"
#include "gromacs/utility/smalloc.h"

using gmx::ArrayRef;
using gmx::RVec;

// TODO This implementation of ensemble orientation restraints is nasty because
// a user can't just do multi-sim with single-sim orientation restraints.

void init_orires(FILE*                 fplog,
                 const gmx_mtop_t*     mtop,
                 const t_inputrec*     ir,
                 const t_commrec*      cr,
                 const gmx_multisim_t* ms,
                 t_state*              globalState,
                 t_oriresdata*         od)
{
    od->nr = gmx_mtop_ftype_count(mtop, F_ORIRES);
    if (0 == od->nr)
    {
        /* Not doing orientation restraints */
        return;
    }

    const int numFitParams = 5;
    if (od->nr <= numFitParams)
    {
        gmx_fatal(FARGS,
                  "The system has %d orientation restraints, but at least %d are required, since "
                  "there are %d fitting parameters.",
                  od->nr, numFitParams + 1, numFitParams);
    }

    if (ir->bPeriodicMols)
    {
        /* Since we apply fitting, we need to make molecules whole and this
         * can not be done when periodic molecules are present.
         */
        gmx_fatal(FARGS,
                  "Orientation restraints can not be applied when periodic molecules are present "
                  "in the system");
    }

    if (PAR(cr))
    {
        gmx_fatal(FARGS,
                  "Orientation restraints do not work with MPI parallelization. Choose 1 MPI rank, "
                  "if possible.");
    }

    GMX_RELEASE_ASSERT(globalState != nullptr, "We need a valid global state in init_orires");

    od->fc  = ir->orires_fc;
    od->nex = 0;
    od->S   = nullptr;
    od->M   = nullptr;
    od->eig = nullptr;
    od->v   = nullptr;

    int*                 nr_ex   = nullptr;
    int                  typeMin = INT_MAX;
    int                  typeMax = 0;
    gmx_mtop_ilistloop_t iloop   = gmx_mtop_ilistloop_init(mtop);
    int                  nmol;
    while (const InteractionLists* il = gmx_mtop_ilistloop_next(iloop, &nmol))
    {
        const int numOrires = (*il)[F_ORIRES].size();
        if (nmol > 1 && numOrires > 0)
        {
            gmx_fatal(FARGS,
                      "Found %d copies of a molecule with orientation restrains while the current "
                      "code only supports a single copy. If you want to ensemble average, run "
                      "multiple copies of the system using the multi-sim feature of mdrun.",
                      nmol);
        }

        for (int i = 0; i < numOrires; i += 3)
        {
            int type = (*il)[F_ORIRES].iatoms[i];
            int ex   = mtop->ffparams.iparams[type].orires.ex;
            if (ex >= od->nex)
            {
                srenew(nr_ex, ex + 1);
                for (int j = od->nex; j < ex + 1; j++)
                {
                    nr_ex[j] = 0;
                }
                od->nex = ex + 1;
            }
            GMX_ASSERT(nr_ex, "Check for allocated nr_ex to keep the static analyzer happy");
            nr_ex[ex]++;

            typeMin = std::min(typeMin, type);
            typeMax = std::max(typeMax, type);
        }
    }
    /* With domain decomposition we use the type index for indexing in global arrays */
    GMX_RELEASE_ASSERT(
            typeMax - typeMin + 1 == od->nr,
            "All orientation restraint parameter entries in the topology should be consecutive");
    /* Store typeMin so we can index array with the type offset */
    od->typeMin = typeMin;

    snew(od->S, od->nex);
    /* When not doing time averaging, the instaneous and time averaged data
     * are indentical and the pointers can point to the same memory.
     */
    snew(od->Dinsl, od->nr);

    if (ms)
    {
        snew(od->Dins, od->nr);
    }
    else
    {
        od->Dins = od->Dinsl;
    }

    if (ir->orires_tau == 0)
    {
        od->Dtav  = od->Dins;
        od->edt   = 0.0;
        od->edt_1 = 1.0;
    }
    else
    {
        snew(od->Dtav, od->nr);
        od->edt   = std::exp(-ir->delta_t / ir->orires_tau);
        od->edt_1 = 1.0 - od->edt;

        /* Extend the state with the orires history */
        globalState->flags |= (1 << estORIRE_INITF);
        globalState->hist.orire_initf = 1;
        globalState->flags |= (1 << estORIRE_DTAV);
        globalState->hist.norire_Dtav = od->nr * 5;
        snew(globalState->hist.orire_Dtav, globalState->hist.norire_Dtav);
    }

    snew(od->oinsl, od->nr);
    if (ms)
    {
        snew(od->oins, od->nr);
    }
    else
    {
        od->oins = od->oinsl;
    }
    if (ir->orires_tau == 0)
    {
        od->otav = od->oins;
    }
    else
    {
        snew(od->otav, od->nr);
    }
    snew(od->tmpEq, od->nex);

    od->nref = 0;
    for (int i = 0; i < mtop->natoms; i++)
    {
        if (getGroupType(mtop->groups, SimulationAtomGroupType::OrientationRestraintsFit, i) == 0)
        {
            od->nref++;
        }
    }
    snew(od->mref, od->nref);
    snew(od->xref, od->nref);
    snew(od->xtmp, od->nref);

    snew(od->eig, od->nex * 12);

    /* Determine the reference structure on the master node.
     * Copy it to the other nodes after checking multi compatibility,
     * so we are sure the subsystems match before copying.
     */
    auto   x    = makeArrayRef(globalState->x);
    rvec   com  = { 0, 0, 0 };
    double mtot = 0.0;
    int    j    = 0;
    for (const AtomProxy atomP : AtomRange(*mtop))
    {
        const t_atom& local = atomP.atom();
        int           i     = atomP.globalAtomNumber();
        if (mtop->groups.groupNumbers[SimulationAtomGroupType::OrientationRestraintsFit].empty()
            || mtop->groups.groupNumbers[SimulationAtomGroupType::OrientationRestraintsFit][i] == 0)
        {
            /* Not correct for free-energy with changing masses */
            od->mref[j] = local.m;
            // Note that only one rank per sim is supported.
            if (isMasterSim(ms))
            {
                copy_rvec(x[i], od->xref[j]);
                for (int d = 0; d < DIM; d++)
                {
                    com[d] += od->mref[j] * x[i][d];
                }
            }
            mtot += od->mref[j];
            j++;
        }
    }
    svmul(1.0 / mtot, com, com);
    if (isMasterSim(ms))
    {
        for (int j = 0; j < od->nref; j++)
        {
            rvec_dec(od->xref[j], com);
        }
    }

    fprintf(fplog, "Found %d orientation experiments\n", od->nex);
    for (int i = 0; i < od->nex; i++)
    {
        fprintf(fplog, "  experiment %d has %d restraints\n", i + 1, nr_ex[i]);
    }

    sfree(nr_ex);

    fprintf(fplog, "  the fit group consists of %d atoms and has total mass %g\n", od->nref, mtot);

    if (ms)
    {
        fprintf(fplog, "  the orientation restraints are ensemble averaged over %d systems\n", ms->nsim);

        check_multi_int(fplog, ms, od->nr, "the number of orientation restraints", FALSE);
        check_multi_int(fplog, ms, od->nref, "the number of fit atoms for orientation restraining", FALSE);
        check_multi_int(fplog, ms, ir->nsteps, "nsteps", FALSE);
        /* Copy the reference coordinates from the master to the other nodes */
        gmx_sum_sim(DIM * od->nref, od->xref[0], ms);
    }

    please_cite(fplog, "Hess2003");
}

void diagonalize_orires_tensors(t_oriresdata* od)
{
    if (od->M == nullptr)
    {
        snew(od->M, DIM);
        for (int i = 0; i < DIM; i++)
        {
            snew(od->M[i], DIM);
        }
        snew(od->eig_diag, DIM);
        snew(od->v, DIM);
        for (int i = 0; i < DIM; i++)
        {
            snew(od->v[i], DIM);
        }
    }

    for (int ex = 0; ex < od->nex; ex++)
    {
        /* Rotate the S tensor back to the reference frame */
        matrix S, TMP;
        mmul(od->R, od->S[ex], TMP);
        mtmul(TMP, od->R, S);
        for (int i = 0; i < DIM; i++)
        {
            for (int j = 0; j < DIM; j++)
            {
                od->M[i][j] = S[i][j];
            }
        }

        int nrot;
        jacobi(od->M, DIM, od->eig_diag, od->v, &nrot);

        int ord[DIM];
        for (int i = 0; i < DIM; i++)
        {
            ord[i] = i;
        }
        for (int i = 0; i < DIM; i++)
        {
            for (int j = i + 1; j < DIM; j++)
            {
                if (gmx::square(od->eig_diag[ord[j]]) > gmx::square(od->eig_diag[ord[i]]))
                {
                    int t  = ord[i];
                    ord[i] = ord[j];
                    ord[j] = t;
                }
            }
        }

        for (int i = 0; i < DIM; i++)
        {
            od->eig[ex * 12 + i] = od->eig_diag[ord[i]];
        }
        for (int i = 0; i < DIM; i++)
        {
            for (int j = 0; j < DIM; j++)
            {
                od->eig[ex * 12 + 3 + 3 * i + j] = od->v[j][ord[i]];
            }
        }
    }
}

void print_orires_log(FILE* log, t_oriresdata* od)
{
    real* eig;

    diagonalize_orires_tensors(od);

    for (int ex = 0; ex < od->nex; ex++)
    {
        eig = od->eig + ex * 12;
        fprintf(log, "  Orientation experiment %d:\n", ex + 1);
        fprintf(log, "    order parameter: %g\n", eig[0]);
        for (int i = 0; i < DIM; i++)
        {
            fprintf(log, "    eig: %6.3f   %6.3f %6.3f %6.3f\n", (eig[0] != 0) ? eig[i] / eig[0] : eig[i],
                    eig[DIM + i * DIM + XX], eig[DIM + i * DIM + YY], eig[DIM + i * DIM + ZZ]);
        }
        fprintf(log, "\n");
    }
}

real calc_orires_dev(const gmx_multisim_t* ms,
                     int                   nfa,
                     const t_iatom         forceatoms[],
                     const t_iparams       ip[],
                     const t_mdatoms*      md,
                     ArrayRef<const RVec>  xWholeMolecules,
                     const rvec            x[],
                     const t_pbc*          pbc,
                     t_fcdata*             fcd,
                     history_t*            hist)
{
    int           nref;
    real          edt, edt_1, invn, pfac, r2, invr, corrfac, wsv2, sw, dev;
    OriresMatEq*  matEq;
    real*         mref;
    double        mtot;
    rvec *        xref, *xtmp, com, r_unrot, r;
    t_oriresdata* od;
    gmx_bool      bTAV;
    const real    two_thr = 2.0 / 3.0;

    od = &(fcd->orires);

    if (od->nr == 0)
    {
        /* This means that this is not the master node */
        gmx_fatal(FARGS,
                  "Orientation restraints are only supported on the master rank, use fewer ranks");
    }

    bTAV  = (od->edt != 0);
    edt   = od->edt;
    edt_1 = od->edt_1;
    matEq = od->tmpEq;
    nref  = od->nref;
    mref  = od->mref;
    xref  = od->xref;
    xtmp  = od->xtmp;

    if (bTAV)
    {
        od->exp_min_t_tau = hist->orire_initf * edt;

        /* Correction factor to correct for the lack of history
         * at short times.
         */
        corrfac = 1.0 / (1.0 - od->exp_min_t_tau);
    }
    else
    {
        corrfac = 1.0;
    }

    if (ms)
    {
        invn = 1.0 / ms->nsim;
    }
    else
    {
        invn = 1.0;
    }

    clear_rvec(com);
    mtot  = 0;
    int j = 0;
    for (int i = 0; i < md->nr; i++)
    {
        if (md->cORF[i] == 0)
        {
            copy_rvec(xWholeMolecules[i], xtmp[j]);
            mref[j] = md->massT[i];
            for (int d = 0; d < DIM; d++)
            {
                com[d] += mref[j] * xtmp[j][d];
            }
            mtot += mref[j];
            j++;
        }
    }
    svmul(1.0 / mtot, com, com);
    for (int j = 0; j < nref; j++)
    {
        rvec_dec(xtmp[j], com);
    }
    /* Calculate the rotation matrix to rotate x to the reference orientation */
    calc_fit_R(DIM, nref, mref, xref, xtmp, od->R);

    for (int fa = 0; fa < nfa; fa += 3)
    {
        const int type           = forceatoms[fa];
        const int restraintIndex = type - od->typeMin;
        if (pbc)
        {
            pbc_dx_aiuc(pbc, x[forceatoms[fa + 1]], x[forceatoms[fa + 2]], r_unrot);
        }
        else
        {
            rvec_sub(x[forceatoms[fa + 1]], x[forceatoms[fa + 2]], r_unrot);
        }
        mvmul(od->R, r_unrot, r);
        r2   = norm2(r);
        invr = gmx::invsqrt(r2);
        /* Calculate the prefactor for the D tensor, this includes the factor 3! */
        pfac = ip[type].orires.c * invr * invr * 3;
        for (int i = 0; i < ip[type].orires.power; i++)
        {
            pfac *= invr;
        }
        rvec5& Dinsl = od->Dinsl[restraintIndex];
        Dinsl[0]     = pfac * (2 * r[0] * r[0] + r[1] * r[1] - r2);
        Dinsl[1]     = pfac * (2 * r[0] * r[1]);
        Dinsl[2]     = pfac * (2 * r[0] * r[2]);
        Dinsl[3]     = pfac * (2 * r[1] * r[1] + r[0] * r[0] - r2);
        Dinsl[4]     = pfac * (2 * r[1] * r[2]);

        if (ms)
        {
            for (int i = 0; i < 5; i++)
            {
                od->Dins[restraintIndex][i] = Dinsl[i] * invn;
            }
        }
    }

    if (ms)
    {
        gmx_sum_sim(5 * od->nr, od->Dins[0], ms);
    }

    /* Calculate the order tensor S for each experiment via optimization */
    for (int ex = 0; ex < od->nex; ex++)
    {
        for (int i = 0; i < 5; i++)
        {
            matEq[ex].rhs[i] = 0;
            for (int j = 0; j <= i; j++)
            {
                matEq[ex].mat[i][j] = 0;
            }
        }
    }

    for (int fa = 0; fa < nfa; fa += 3)
    {
        const int type           = forceatoms[fa];
        const int restraintIndex = type - od->typeMin;
        rvec5&    Dtav           = od->Dtav[restraintIndex];
        if (bTAV)
        {
            /* Here we update Dtav in t_fcdata using the data in history_t.
             * Thus the results stay correct when this routine
             * is called multiple times.
             */
            for (int i = 0; i < 5; i++)
            {
                Dtav[i] = edt * hist->orire_Dtav[restraintIndex * 5 + i]
                          + edt_1 * od->Dins[restraintIndex][i];
            }
        }

        int  ex     = ip[type].orires.ex;
        real weight = ip[type].orires.kfac;
        /* Calculate the vector rhs and half the matrix T for the 5 equations */
        for (int i = 0; i < 5; i++)
        {
            matEq[ex].rhs[i] += Dtav[i] * ip[type].orires.obs * weight;
            for (int j = 0; j <= i; j++)
            {
                matEq[ex].mat[i][j] += Dtav[i] * Dtav[j] * weight;
            }
        }
    }
    /* Now we have all the data we can calculate S */
    for (int ex = 0; ex < od->nex; ex++)
    {
        OriresMatEq& eq = matEq[ex];
        /* Correct corrfac and copy one half of T to the other half */
        for (int i = 0; i < 5; i++)
        {
            eq.rhs[i] *= corrfac;
            eq.mat[i][i] *= gmx::square(corrfac);
            for (int j = 0; j < i; j++)
            {
                eq.mat[i][j] *= gmx::square(corrfac);
                eq.mat[j][i] = eq.mat[i][j];
            }
        }
        m_inv_gen(&eq.mat[0][0], 5, &eq.mat[0][0]);
        /* Calculate the orientation tensor S for this experiment */
        matrix& S = od->S[ex];
        S[0][0]   = 0;
        S[0][1]   = 0;
        S[0][2]   = 0;
        S[1][1]   = 0;
        S[1][2]   = 0;
        for (int i = 0; i < 5; i++)
        {
            S[0][0] += 1.5 * eq.mat[0][i] * eq.rhs[i];
            S[0][1] += 1.5 * eq.mat[1][i] * eq.rhs[i];
            S[0][2] += 1.5 * eq.mat[2][i] * eq.rhs[i];
            S[1][1] += 1.5 * eq.mat[3][i] * eq.rhs[i];
            S[1][2] += 1.5 * eq.mat[4][i] * eq.rhs[i];
        }
        S[1][0] = S[0][1];
        S[2][0] = S[0][2];
        S[2][1] = S[1][2];
        S[2][2] = -S[0][0] - S[1][1];
    }

    const matrix* S = od->S;

    wsv2 = 0;
    sw   = 0;

    for (int fa = 0; fa < nfa; fa += 3)
    {
        const int type           = forceatoms[fa];
        const int restraintIndex = type - od->typeMin;
        const int ex             = ip[type].orires.ex;

        const rvec5& Dtav = od->Dtav[restraintIndex];
        od->otav[restraintIndex] =
                two_thr * corrfac
                * (S[ex][0][0] * Dtav[0] + S[ex][0][1] * Dtav[1] + S[ex][0][2] * Dtav[2]
                   + S[ex][1][1] * Dtav[3] + S[ex][1][2] * Dtav[4]);
        if (bTAV)
        {
            const rvec5& Dins = od->Dins[restraintIndex];
            od->oins[restraintIndex] =
                    two_thr
                    * (S[ex][0][0] * Dins[0] + S[ex][0][1] * Dins[1] + S[ex][0][2] * Dins[2]
                       + S[ex][1][1] * Dins[3] + S[ex][1][2] * Dins[4]);
        }
        if (ms)
        {
            /* When ensemble averaging is used recalculate the local orientation
             * for output to the energy file.
             */
            const rvec5& Dinsl = od->Dinsl[restraintIndex];
            od->oinsl[restraintIndex] =
                    two_thr
                    * (S[ex][0][0] * Dinsl[0] + S[ex][0][1] * Dinsl[1] + S[ex][0][2] * Dinsl[2]
                       + S[ex][1][1] * Dinsl[3] + S[ex][1][2] * Dinsl[4]);
        }

        dev = od->otav[restraintIndex] - ip[type].orires.obs;

        wsv2 += ip[type].orires.kfac * gmx::square(dev);
        sw += ip[type].orires.kfac;
    }
    od->rmsdev = std::sqrt(wsv2 / sw);

    /* Rotate the S matrices back, so we get the correct grad(tr(S D)) */
    for (int ex = 0; ex < od->nex; ex++)
    {
        matrix RS;
        tmmul(od->R, od->S[ex], RS);
        mmul(RS, od->R, od->S[ex]);
    }

    return od->rmsdev;

    /* Approx. 120*nfa/3 flops */
}

real orires(int             nfa,
            const t_iatom   forceatoms[],
            const t_iparams ip[],
            const rvec      x[],
            rvec4           f[],
            rvec            fshift[],
            const t_pbc*    pbc,
            real gmx_unused lambda,
            real gmx_unused* dvdlambda,
            const t_mdatoms gmx_unused* md,
            t_fcdata*                   fcd,
            int gmx_unused* global_atom_index)
{
    int                 ex, power, ki = CENTRAL;
    real                r2, invr, invr2, fc, smooth_fc, dev, devins, pfac;
    rvec                r, Sr, fij;
    real                vtot;
    const t_oriresdata* od;
    gmx_bool            bTAV;

    vtot = 0;
    od   = &(fcd->orires);

    if (od->fc != 0)
    {
        bTAV = (od->edt != 0);

        smooth_fc = od->fc;
        if (bTAV)
        {
            /* Smoothly switch on the restraining when time averaging is used */
            smooth_fc *= (1.0 - od->exp_min_t_tau);
        }

        for (int fa = 0; fa < nfa; fa += 3)
        {
            const int type           = forceatoms[fa];
            const int ai             = forceatoms[fa + 1];
            const int aj             = forceatoms[fa + 2];
            const int restraintIndex = type - od->typeMin;
            if (pbc)
            {
                ki = pbc_dx_aiuc(pbc, x[ai], x[aj], r);
            }
            else
            {
                rvec_sub(x[ai], x[aj], r);
            }
            r2    = norm2(r);
            invr  = gmx::invsqrt(r2);
            invr2 = invr * invr;
            ex    = ip[type].orires.ex;
            power = ip[type].orires.power;
            fc    = smooth_fc * ip[type].orires.kfac;
            dev   = od->otav[restraintIndex] - ip[type].orires.obs;

            /* NOTE:
             * there is no real potential when time averaging is applied
             */
            vtot += 0.5 * fc * gmx::square(dev);

            if (bTAV)
            {
                /* Calculate the force as the sqrt of tav times instantaneous */
                devins = od->oins[restraintIndex] - ip[type].orires.obs;
                if (dev * devins <= 0)
                {
                    dev = 0;
                }
                else
                {
                    dev = std::sqrt(dev * devins);
                    if (devins < 0)
                    {
                        dev = -dev;
                    }
                }
            }

            pfac = fc * ip[type].orires.c * invr2;
            for (int i = 0; i < power; i++)
            {
                pfac *= invr;
            }
            mvmul(od->S[ex], r, Sr);
            for (int i = 0; i < DIM; i++)
            {
                fij[i] = -pfac * dev * (4 * Sr[i] - 2 * (2 + power) * invr2 * iprod(Sr, r) * r[i]);
            }

            for (int i = 0; i < DIM; i++)
            {
                f[ai][i] += fij[i];
                f[aj][i] -= fij[i];
                if (fshift)
                {
                    fshift[ki][i] += fij[i];
                    fshift[CENTRAL][i] -= fij[i];
                }
            }
        }
    }

    return vtot;

    /* Approx. 80*nfa/3 flops */
}

void update_orires_history(const t_fcdata* fcd, history_t* hist)
{
    const t_oriresdata* od = &(fcd->orires);

    if (od->edt != 0)
    {
        /* Copy the new time averages that have been calculated
         *  in calc_orires_dev.
         */
        hist->orire_initf = od->exp_min_t_tau;
        for (int pair = 0; pair < od->nr; pair++)
        {
            for (int i = 0; i < 5; i++)
            {
                hist->orire_Dtav[pair * 5 + i] = od->Dtav[pair][i];
            }
        }
    }
}
